As you can see I have removed all unnecessary files from previous post. These are only things that you need to run ASP.NET Core stuff on your machine.
UserController is our REST Service from last post. In web part I have left only static html file which will be calling this service.

JSON as Service Result

A bit surprising, but on .NET Core returning JSON works without much problems and any addtional libraries.

Calling REST Service via jQuery

Should be pretty simple… I found it on StackOverflow (index.html)
A lot of html and very simple call. What we get?

XMLHttpRequest cannot load http://localhost:5000/api/user. No 'Access-Control-Allow-Origin' header is present on the requested resource. Origin 'null' is therefore not allowed access.

Que… CORS

Shortly, browser won’t allow you to make a call from different domain. It’s of course more complicated and you can start reading in wikipedia: https://en.wikipedia.org/wiki/Cross-origin_resource_sharing
But the real question is, how to resolve it?Whatever you will find in google won’t work
This may be simplification, but the problem is that .NET team changes their API more frequently then JavaScript teams.
Here is a solution that is compatible with rc1-update1